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Journal of Lie Theory 11 (2001), No. 1, 173--184
Copyright Heldermann Verlag 2001

Explicit Formulae for Cocycles of Holomorphic Vector Fields with Values in λ Densities

Friedrich Wagemann
Institut G. Desargues, Université C. Bernard - Lyon 1, 43, Blv. du 11 Novembre 1918, 69622 Villeurbanne, France

We give explicit formulae for the generators of H2( Hol (Σr),  Fλr)) in terms of affine and projective connections, Σr being a compact Riemann surface punctured in r points. This is done using the cocycles which have been evidenced by V. Ovsienko and C. Roger ["Generalizations of Virasoro group and Virasoro algebra through extensions by modules of tensor-densities on S1, Indag. Math., N.S. 9 (1998) 277--288] and globalizing them by their transformation property.

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